Fellow in Quantitative Methodology
London School of Economics
10 minute break
1 hour lunch break
10 minute break
“no causation without manipulation.”
-Rubin (1975)
Define treatment T:
Define potential outcomes:
Causal Effect:
\[ Causal \, Effect = Y(1) - Y(0) \]
Problem: We can only observe one of these!
| Unit | Treated? (T) | Observed Outcome | Counterfactual Outcome |
|---|---|---|---|
| A | 1 | ( Y_A(1) ) | ( Y_A(0) ) (Missing) |
| B | 0 | ( Y_B(0) ) | ( Y_B(1) ) (Missing) |
We’ll explore these in later sessions!
📌 Questions? Feel free to ask!
source: Brophy (2021)
Definition: Confounding occurs when a third variable (a confounder) influences both the treatment and the outcome, creating a spurious association.
Problem: Confounders are pre-treatment variables that affect both treatment assignment and the outcome.
Effect: Confounding distorts the causal effect because it makes it unclear whether the observed effect is due to the treatment or the confounding variable.
Confounding is not based on statistical associations, but on qualitative knowledge of the data.
RQ: Does job training increase salary?
Definition: Selection bias occurs when the sample used in the analysis is not representative of the population due to a non-random selection process
Problem: Arises when the probability of being included in the study depends on the treatment, the outcome, or factors related to both.
Effect: Creates spurious associations between the treatment and outcome that do not reflect the true causal effect.
This is more challenging than confounding because it is not based on pre-treatment variables
Solutions:
Bonus: Create a DAG
We want to keep returning to this ideal when designing observational studies.
Does a new training programme increase employment rates?
The UK Government introduces a training programme to increase employment. The programme is rolled out to local authorities at different times. We want to estimate the causal effect of the programme on employment rates.
Many policies assign treatment based on a threshold. RD estimates causal effects by comparing outcomes just above and below the threshold.
Does the size of a seminar group affect student performance?
The maximum number of students per seminar group at LSE is 30. We want to know whether seminar group size affects student performance. We compare student performance just above and below the threshold.
Does college education increase earnings?
There are many reasons why people choose to go to college, such as ability, motivation, and family background. One factor that may affect college attendance is proximity to a college. We can use proximity to a college as an instrument for college attendance (Card 1993)
Full Example:
In April 2020 during the height of the COVID pandemic, Donald Trump sent three messages on Twitter calling for the “liberation” of three specific states under lockdown. We want to estimate the causal effect of these tweets on social distancing behavior.
What assumptions do we need to identify the causal effect of Trump’s tweets on social distancing behavior?
where:
Github Repository: Causal Inference Methods for Observational Data
This notebook is available in the Github repository Code folder titled DID_notebook.qmd